Atmospheric balloons are constructed with longitudinal tendons and pliable materials cut and bonded to achieve a desired shape (e.g., a lobed pumpkin shape). Atmospheric balloons and other articles are inflated and maintained for long periods of time. In some examples gores are cut and assembled to form the lobes of the balloon membrane, for instance with a constant lobe radius or constant lobe angle construction method. The lobed shape of the constant lobe angle or constant lobe radius gores is configured to mitigate hoop stress on the materials and joints of the balloon.
An atmospheric balloon or article including constant lobe angle type gores uses lofted curves to form the constant lobe angle of the gore from the upper and lower ends of the gore (e.g., the apexes of a balloon) to the balloon equator. Stated another way, when measured from one edge of the gore to the opposed edge the constant lobe angle gore (a component gore of an overall balloon or article) will have a constant angular measurement between the each of the opposed sides from the apexes to the equator (or midpoint) of the gore. To achieve this constant angular measurement the gore material is cut with a precise mathematically derived curved line pattern along each of the opposed edges. The curved line pattern is generated according to mathematical formulae and is based on the desired length and width of the balloon or article. When the gore, cut with the curved line pattern, is incorporated into a balloon and the balloon is inflated the angular measurement between the opposed edges of the gore remains the same from the apexes to the equator while the effective radius of the arc of the gore material changes from the apexes to the equator (increases).
Another example of an atmospheric balloon includes gores constructed with a constant lobe radius type gores that use lofted curves to provide a constant lobe radius. In contrast to the constant lobe angle gores, the constant lobe radius gores have a constant radius (when the balloon or article is inflated) from the apexes to the equator while the angular measurements of the constant lobe radius gores vary. For instance, the constant lobe radius gores have a constant radius measurement (based on the shape of the arc of the gore relative to a center point of the arc) from the apexes to the equator while the angle measurements between the opposed edges of the gore increase from the apexes to the equator. In a similar manner to the constant lobe angle gores described above, the constant lobe radius gores are constructed by cutting the gore material along a precise mathematically derived curved line pattern (based on the desired length and width of the balloon or article) that ensures, when inflated, the gore will have a constant lobe radius.